MathematicsGrade 10en

📐 Distance and Midpoint Formulas

Master the distance and midpoint formulas in the coordinate plane to solve real-world and abstract geometry problems. **What you'll learn:** - Apply the distance formula to find the length between two points - Calculate midpoints of line segments using the midpoint formula - Solve multi-step problems combining both formulas - Work with negative coordinates and non-integer results - Verify geometric properties using distance and midpoint calculations

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Questions in this quiz

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Question 1
What is the distance between the points $(3, 4)$ and $(0, 0)$ ?
Question 2
What is the midpoint of the line segment connecting $(2, 6)$ and $(8, 10)$ ?
Question 3
The distance between $(1, 2)$ and $(4, 6)$ is $\sqrt{___}$ .
Question 4
The midpoint of a segment with endpoints $(-3, 5)$ and $(3, -5)$ is $(0, 0)$ .
Question 5
Points $A(-2, 3)$ and $B(4, -1)$ form a line segment. What is the distance between them?
Question 6
If the midpoint of a segment is $(2, -3)$ and one endpoint is $(5, 1)$ , what is the other endpoint?
Question 7
Triangle $PQR$ has vertices $P(0, 0)$ , $Q(6, 0)$ , and $R(3, 4)$ . Which statement about the distances is true?
Question 8
A circle has its center at the midpoint of the segment connecting $(-4, 2)$ and $(2, 8)$ . The center is at $(___, ___)$ .
Question 9
A square has vertices at $(0, 0)$ , $(5, 0)$ , $(5, 5)$ , and $(0, 5)$ . What is the distance along the diagonal from $(0, 0)$ to $(5, 5)$ ?
Question 10
Points $C(-5, -2)$ , $D(1, 4)$ , and $E$ form a triangle where $D$ is the midpoint of segment $CE$ . If the distance $|CD| = \sqrt{52}$ , what are the coordinates of $E$ ?